Problem 17 - Algebra 1: Concepts and Skills

Question

Write the phrase as a variable expression. Let x represent the number. A number plus 18

Step-by-Step Solution

Answer

The algebraic expression for the phrase 'A number plus 18' is 'x + 18'.

Step 1: Identify the variable

In the given phrase, the 'number' is represented by a variable. In this case, according to the exercise, the variable is 'x'.

Step 2: Understand the operation

The word 'plus' in the phrase represents the mathematical operation of addition.

Step 3: Write the phrase as a variable expression

Combining the variable and the operation, the phrase 'A number plus 18' can be written as the variable expression 'x + 18' in algebraic form.

Key Concepts

Algebraic Expressions

Algebraic expressions are the backbone of algebra and serve as a way to represent relationships using symbols and numbers. They consist of variables, constants, and operation symbols that come together to form a meaningful combination. For instance, the expression \( x + 18 \) contains a variable \( x \)—standing in for an unknown number—and a constant \( 18 \) which is a specific known value in this equation.

Understanding algebraic expressions is crucial as they can represent real-world quantities and their relationships. Instead of working with specific numbers, algebra allows us to work in general terms, providing a powerful tool to solve a variety of problems with unknown quantities.

Translating Verbal Phrases to Algebra

Translating verbal phrases into algebraic expressions is an essential skill in algebra. It entails converting words into symbols and ensures that the original problem's meaning is preserved. To master this translation, it's vital to recognize key terms that indicate specific operations: 'plus' suggests addition, 'minus' points to subtraction, 'product of' hints multiplication, and 'quotient of' indicates division.

Let's consider the phrase 'a number plus 18'. Here, the term 'a number' is open-ended and can represent any value—making it a perfect candidate for a variable like \( x \). The word 'plus' is the signal to add, and '18' is a specific numeric value. Accordingly, we translate the phrase to \( x + 18 \). This ability to switch between verbal statements and algebraic expressions is essential for problem-solving in various algebraic contexts.

Basic Algebra Operations

The four basic operations of algebra mirror those of arithmetic: addition, subtraction, multiplication, and division. Each of these operations has its own symbol and set of rules. In algebra, however, we operate with variables as well as numbers.

When we add or subtract, we combine or separate quantities, respectively. For multiplication, we use the 'times' symbol (\(\times\)) or parentheses to show repeated addition of the same number or variable. Division is written with a divide symbol (\(\div\)) or as a fraction.

Understanding how to use these operations with variables is essential. For example, if we multiply a variable \( x \) by \( 3 \), we write it as \( 3x \). Likewise, if we divide \( x \) by \( 4 \), it becomes \( \frac{x}{4} \). These operations allow us to construct and manipulate algebraic expressions to model and solve real-world problems.